This article is an introduction to Malliavin Calculus for practitioners. We treat one specific application to the calculation of greeks in Finance. We consider also the kernel density method to compute greeks and an extension of the Vega index called the local vega index.

In this article, we develop a Malliavin calculus associated to a timecontinuous Markov chain with finite state space. We apply it to get a criterion of density for solutions of SDE involving the Markov chain and also to compute greeks. keywords: Dirichlet form; Integration by parts formula; Malliavin calculus; Markov chain; computation of greeks. Mathematics subject classification: 60H07; 60J10...

We show how algorithmic differentiation can be used to efficiently implement the pathwise derivative method for the calculation of option sensitivities using Monte Carlo simulations. The main practical difficulty of the pathwise derivative method is that it requires the differentiation of the payout function. For the type of structured options for which Monte Carlo simulations are usually emplo...

In this article, we give a brief informal introduction to Malliavin Calculus for newcomers. We apply these ideas to the simulation of Greeks in Finance. First to European-type options where formulas can be computed explicitly and therefore can serve as testing ground. Later we study the case of Asian options where close formulas are not available, and we also open the view for including more ex...

The derivatives of option prices with respect to underlying parameters are commonly referred to as Greeks, and they measure the sensitivities of option prices to these parameters. When the closed-form solutions for option prices do not exist and the discounted payoff functions of the options are not sufficiently smooth, estimating Greeks is computationally challenging and could be a burdensome ...

In this paper we develop an algorithm to calculate prices and Greeks of barrier options driven by a class of additive processes. Additive processes are time-inhomogeneous Lévy processes, or equivalently, processes with independent but inhomogeneous increments. We obtain an explicit semi-analytical expression for the first-passage probability of an additive process with hyper-exponential jumps. ...